		Search-engine friendly clone of the ACL2 documentation.

Curve-parameterization

Curve

Fixtype of curve choices.

For now there is just one choice, namely Edwards BLS12.

Definitions and Theorems

Function: curve-equiv$inline

(defun curve-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (curvep acl2::x)
                              (curvep acl2::y))))
  (equal (curve-fix acl2::x)
         (curve-fix acl2::y)))

Theorem: curve-equiv-is-an-equivalence

(defthm curve-equiv-is-an-equivalence
  (and (booleanp (curve-equiv x y))
       (curve-equiv x x)
       (implies (curve-equiv x y)
                (curve-equiv y x))
       (implies (and (curve-equiv x y)
                     (curve-equiv y z))
                (curve-equiv x z)))
  :rule-classes (:equivalence))

Theorem: curve-equiv-implies-equal-curve-fix-1

(defthm curve-equiv-implies-equal-curve-fix-1
  (implies (curve-equiv acl2::x x-equiv)
           (equal (curve-fix acl2::x)
                  (curve-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: curve-fix-under-curve-equiv

(defthm curve-fix-under-curve-equiv
  (curve-equiv (curve-fix acl2::x)
               acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-curve-fix-1-forward-to-curve-equiv

(defthm equal-of-curve-fix-1-forward-to-curve-equiv
  (implies (equal (curve-fix acl2::x) acl2::y)
           (curve-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-curve-fix-2-forward-to-curve-equiv

(defthm equal-of-curve-fix-2-forward-to-curve-equiv
  (implies (equal acl2::x (curve-fix acl2::y))
           (curve-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: curve-equiv-of-curve-fix-1-forward

(defthm curve-equiv-of-curve-fix-1-forward
  (implies (curve-equiv (curve-fix acl2::x)
                        acl2::y)
           (curve-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: curve-equiv-of-curve-fix-2-forward

(defthm curve-equiv-of-curve-fix-2-forward
  (implies (curve-equiv acl2::x (curve-fix acl2::y))
           (curve-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Subtopics

Curvep: Recognizer for curve.
Curve-fix: Fixer for curve.